Approaching MIMO channel capacity with reduced-complexity soft sphere decoding

Hard Sphere-Decoding (SD) has well appreciated merits for near-optimal demodulation of multiuser, block single-antenna, or, multi-antenna transmissions over multi-input multi-output (MIMO) channels. At increased complexity, a soft version of SD, so termed list SD (LSD), has been recently applied to coded layered space-time (LSI) systems enabling them to approach MIMO channel capacity. By introducing a novel bit-level multi-stream LST transmitter along with a soft-to-hard decoder conversion, we show how to achieve the near-capacity performance of LSD at reduced complexity, and even outperform it as the size of the block to be decoded (M) increases. Specifically, for binary real LST codes we develop exact max-log based SD schemes with average complexity O(M ⁴), and various approximate alternatives trading-off performance for average complexity down to O(M³). These schemes apply directly to the real and imaginary parts of QPSK signalling, and also to QAM signalling after incorporating an appropriate interference estimation and cancellation module. We corroborate our reduced-complexity near-optimal soft SD algorithms with simulations.